How many diagonals does a polygon with 10 sides have? How many sides does a polygon with 152 diagonals have?

Answer 1

A triangle has 0 diagonals.
A square has 2
A pentagon has 5
A hexagon has 9

How do we get these? A diagonal goes from a vertex to any other vertex that is not itself or next to itself, so for an ngon there are n - 3 such lines. However, since each diagonal is counted twice (once for each end), you need to divide by 2 to get the actual number. So, the formula is

n*(n-3)/2

So, a 10-gon would have 35 diagonals.

152 = (n^2 - 3n)/2
n^2 - 3n - 304 = 0
(n + 16)(n - 19) = 0
So a 19-gon has 152 diagonals.

Answer 2

In general a polygon of n sides has

Number of diagonals = Comb of n taken by two - n=

n(n-1)/2-n =(n^2-3n)/2

if this =152 n^2 -3n -304 = 0 Applying 2nd degree equ.formula as n must be positive n=19

Answer 3

to find how many diagnals there are use this formula....
n(n-3)/2 where n is the number of polygon sides.

10(10-3)/2
(100-30)/2
70/2 = 35


152(152-3)/2
(23104-456)/2
22648/2 = 11324


hope that hepled

Answer 4

The formula n(n-3)/2 comes from this formula:
sum of integers = 1+2+3+..+n = n(n-1)/2